Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalog of designs with two-level factors as well as four-level factors. To create the catalog, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of non-isomorphic designs. Finally, we use the most efficient method to generate a catalog of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalog by revisiting the motivating examples.
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This paper presents an efficient algorithm for the sequential positioning, also called nested dissection, of two planes in an arbitrary polyhedron. Two planar interfaces are positioned such that the first plane truncates a given volume from this arbitrary polyhedron and the next plane truncates a second given volume from the residual polyhedron. This is a relevant task in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid (VoF) method with a Piecewise Linear Interface Calculation (PLIC). An efficient algorithm for this task significantly speeds up the three-phase PLIC algorithm. The present study describes a method based on a recursive application of the Gaussian divergence theorem, where the fact that the truncated polyhedron shares multiple faces with the original polyhedron can be exploited to reduce the computational effort. A careful choice of the coordinate system origin for the volume computation allows for successive positioning of two planes without reestablishing polyhedron connectivity. Combined with a highly efficient root finding, this results in a significant performance gain in the reconstruction of the three-phase interface configurations. The performance of the new method is assessed in a series of carefully designed numerical experiments. Compared to a conventional decomposition-based approach, the number of iterations and, thus, of the required truncations was reduced by up to an order of magnitude. The PLIC positioning run-time was reduced by about 90% in our reference implementation. Integrated into the multi-phase flow solver Free Surface 3D (FS3D), an overall performance gain of about 20% was achieved. Allowing for simple integration into existing numerical schemes, the proposed algorithm is self-contained (example Fortran Module see //doi.org/10.18419/darus-2488), requiring no external decomposition libraries.
Stock selection is important for investors to construct profitable portfolios. Graph neural networks (GNNs) are increasingly attracting researchers for stock prediction due to their strong ability of relation modelling and generalisation. However, the existing GNN methods only focus on simple pairwise stock relation and do not capture complex higher-order structures modelling relations more than two nodes. In addition, they only consider factors of technical analysis and overlook factors of fundamental analysis that can affect the stock trend significantly. Motivated by them, we propose higher-order graph attention network with joint analysis (H-GAT). H-GAT is able to capture higher-order structures and jointly incorporate factors of fundamental analysis with factors of technical analysis. Specifically, the sequential layer of H-GAT take both types of factors as the input of a long-short term memory model. The relation embedding layer of H-GAT constructs a higher-order graph and learn node embedding with GAT. We then predict the ranks of stock return. Extensive experiments demonstrate the superiority of our H-GAT method on the profitability test and Sharp ratio over both NSDAQ and NYSE datasets
Text-to-image generation models represent the next step of evolution in image synthesis, offering a natural way to achieve flexible yet fine-grained control over the result. One emerging area of research is the fast adaptation of large text-to-image models to smaller datasets or new visual concepts. However, many efficient methods of adaptation have a long training time, which limits their practical applications, slows down research experiments, and spends excessive GPU resources. In this work, we study the training dynamics of popular text-to-image personalization methods (such as Textual Inversion or DreamBooth), aiming to speed them up. We observe that most concepts are learned at early stages and do not improve in quality later, but standard model convergence metrics fail to indicate that. Instead, we propose a simple drop-in early stopping criterion that only requires computing the regular training objective on a fixed set of inputs for all training iterations. Our experiments on Stable Diffusion for a range of concepts and for three personalization methods demonstrate the competitive performance of our approach, making adaptation up to 8 times faster with no significant drops in quality.
While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating process and (iii) allow for coherent post-hoc analyses. In particular, most existing methods assume Gaussianity or equal covariance functions across groups (homoscedasticity) and are only applicable for specific study designs that do not allow for evaluation of interactions. Moreover, all available strategies are only designed for testing global hypotheses and do not directly allow a more in-depth analysis of multiple local hypotheses. To address the first two problems (i)-(ii), we propose flexible integral-type test statistics that are applicable in general factorial designs under minimal assumptions on the data generating process. In particular, we neither postulate homoscedasticity nor Gaussianity. To approximate the statistics' null distribution, we adopt a resampling approach and validate it methodologically. Finally, we use our flexible testing framework to (iii) infer several local null hypotheses simultaneously. To allow for powerful data analysis, we thereby take the complex dependencies of the different local test statistics into account. In extensive simulations we confirm that the new methods are flexibly applicable. Two illustrate data analyses complete our study. The new testing procedures are implemented in the R package multiFANOVA, which will be available on CRAN soon.
Connectionist Temporal Classification (CTC) model is a very efficient method for modeling sequences, especially for speech data. In order to use CTC model as an Automatic Speech Recognition (ASR) task, the beam search decoding with an external language model like n-gram LM is necessary to obtain reasonable results. In this paper we analyze the blank label in CTC beam search deeply and propose a very simple method to reduce the amount of calculation resulting in faster beam search decoding speed. With this method, we can get up to 78% faster decoding speed than ordinary beam search decoding with a very small loss of accuracy in LibriSpeech datasets. We prove this method is effective not only practically by experiments but also theoretically by mathematical reasoning. We also observe that this reduction is more obvious if the accuracy of the model is higher.
The calibration of the EFL teaching and learning approaches with Artificial Intelligence can potentially facilitate a smart transformation, fostering a personalized and engaging experience in teaching and learning among the stakeholders. The paper focuses on developing an EFL Big Data Ecosystem that is based on Big Data, Analytics, Machine Learning and cluster domain of EFL teaching and learning contents. Accordingly, the paper uses two membranes to construe its framework, namely (i) Open Big Data Membrane that stores random data collected from various source domains and (ii) Machine Learning Membrane that stores specially prepared structured and semi-structured data. Theoretically, the structured and semi structured data are to be prepared skill-wise, attribute-wise, method-wise, and preference-wise to accommodate the personalized preferences and diverse teaching and learning needs of different individuals. The ultimate goal is to optimize the learning experience by leveraging machine learning to create tailored content that aligns with the diverse teaching and learning needs of the EFL communities.
The rapid advancement of Large Language Models (LLMs) has led to extensive discourse regarding their potential to boost the return of quantitative stock trading strategies. This discourse primarily revolves around harnessing the remarkable comprehension capabilities of LLMs to extract sentiment factors which facilitate informed and high-frequency investment portfolio adjustments. To ensure successful implementations of these LLMs into the analysis of Chinese financial texts and the subsequent trading strategy development within the Chinese stock market, we provide a rigorous and encompassing benchmark as well as a standardized back-testing framework aiming at objectively assessing the efficacy of various types of LLMs in the specialized domain of sentiment factor extraction from Chinese news text data. To illustrate how our benchmark works, we reference three distinctive models: 1) the generative LLM (ChatGPT), 2) the Chinese language-specific pre-trained LLM (Erlangshen-RoBERTa), and 3) the financial domain-specific fine-tuned LLM classifier(Chinese FinBERT). We apply them directly to the task of sentiment factor extraction from large volumes of Chinese news summary texts. We then proceed to building quantitative trading strategies and running back-tests under realistic trading scenarios based on the derived sentiment factors and evaluate their performances with our benchmark. By constructing such a comparative analysis, we invoke the question of what constitutes the most important element for improving a LLM's performance on extracting sentiment factors. And by ensuring that the LLMs are evaluated on the same benchmark, following the same standardized experimental procedures that are designed with sufficient expertise in quantitative trading, we make the first stride toward answering such a question.
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. A randomized group-regularized optimization problem is studied. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.
This paper presents a comprehensive exploration of leveraging Large Language Models (LLMs), specifically GPT-4, in the field of instructional design. With a focus on scaling evidence-based instructional design expertise, our research aims to bridge the gap between theoretical educational studies and practical implementation. We discuss the benefits and limitations of AI-driven content generation, emphasizing the necessity of human oversight in ensuring the quality of educational materials. This work is elucidated through two detailed case studies where we applied GPT-4 in creating complex higher-order assessments and active learning components for different courses. From our experiences, we provide best practices for effectively using LLMs in instructional design tasks, such as utilizing templates, fine-tuning, handling unexpected output, implementing LLM chains, citing references, evaluating output, creating rubrics, grading, and generating distractors. We also share our vision of a future recommendation system, where a customized GPT-4 extracts instructional design principles from educational studies and creates personalized, evidence-supported strategies for users' unique educational contexts. Our research contributes to understanding and optimally harnessing the potential of AI-driven language models in enhancing educational outcomes.
In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work (Li et al. 2022): (1) the conservation of the Jacobi integral, and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.
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